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Hardy, Godfrey H. (1877 - 1947)

The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.

A Mathematician's Apology, London, Cambridge University Press, 1941.

Hardy, Godfrey H. (1877 - 1947)

A science is said to
be useful if its
development tends to
accentuate the
existing
inequalities in the
distribution of
wealth, or more
directly promotes
the destruction of
human life.

Hardy, Godfrey H. (1877 - 1947)

There is no scorn more profound, or on the whole more justifiable, than that of the men who make for the men who explain. Exposition, criticism, appreciation, is work for second-rate minds.

A Mathematician's Apology, London, Cambridge University Press, 1941.

Hardy, Godfrey H. (1877 - 1947)

In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy.

A Mathematician's Apology, London, Cambridge University Press, 1941.

Hardy, Godfrey H. (1877 - 1947)

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.

Hardy, Godfrey H. (1877 - 1947)

I am interested in mathematics only as a creative art.

A Mathematician's Apology, London, Cambridge University Press, 1941.

Hardy, Godfrey H. (1877 - 1947)

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

A Mathematician's Apology, London, Cambridge University Press, 1941.

Hardy, Godfrey H. (1877 - 1947)

[On Ramanujan:]I remember once
going to see him
when he was lying
ill at Putney. I had
ridden in taxi cab
number 1729 and
remarked that the
number seemed to me
rather a dull one,
and that I hoped it
was not an
unfavorable omen.
"No," he replied,
"it is a very
interesting number;
it is the smallest
number expressible
as the sum of two
cubes in two
different ways."

Ramanujan, London:
Cambridge University
Press, 1940.

Hamming, Richard W.

Mathematics is an interesting intellectual sport but it should not be allowed to stand in the way of obtaining sensible information about physical processes.